Most interestingly, we observe that when the price moves in a favorable direction toward in-the-money (i.e., \(dW_t > 0\) ), the policy becomes more risk-averse (i.e., \(dQ_t < 0\)  since \(g^\star (x,q) < 0\) ) and hence it trades more aggressively.
This formally characterizes aggressiveness-in-the-money, which has been observed by [1]}, [2]}, [3]}, [4]}.
Intuitively, if the trader has made some “free” money due to the price change, he would have an additional incentive to complete the liquidation early so as to secure his current profit, and thus he would be willing to pay an additional deterministic cost for aggressive execution.
